# Training Multilayer Perceptrons by Sampling with Quantum Annealers

arXiv: https://arxiv.org/abs/2303.12352 · HTML: https://mlsanity.com/paper/2303.12352/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 44 references that are in the map.
- First posted on arXiv 22 Mar 2023.

## Builds on (most cited first, 16 of 16)

- [Rich feature hierarchies for accurate object detection and semantic segmentation](https://mlsanity.com/paper/1311.2524/) (2013)
- [Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network](https://mlsanity.com/paper/1808.03314/) (2018)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [Application of Quantum Annealing to Training of Deep Neural Networks](https://mlsanity.com/paper/1510.06356/) (2015)
- [Quantum Permutation Synchronization](https://mlsanity.com/paper/2101.07755/) (2021)
- [Q-Match: Iterative Shape Matching via Quantum Annealing](https://mlsanity.com/paper/2105.02878/) (2021)
- [Quantum-Assisted Learning of Hardware-Embedded Probabilistic Graphical Models](https://mlsanity.com/paper/1609.02542/) (2016)
- [Adiabatic Quantum Computing for Multi Object Tracking](https://mlsanity.com/paper/2202.08837/) (2022)
- [Adiabatic Quantum Graph Matching with Permutation Matrix Constraints](https://mlsanity.com/paper/2107.04032/) (2021)
- [Training and Classification using a Restricted Boltzmann Machine on the D-Wave 2000Q](https://mlsanity.com/paper/2005.03247/) (2020)
- [A Hybrid Quantum-Classical Algorithm for Robust Fitting](https://mlsanity.com/paper/2201.10110/) (2022)
- [A Path Towards Quantum Advantage in Training Deep Generative Models with Quantum Annealers](https://mlsanity.com/paper/1912.02119/) (2019)
- [Quantum Annealing Formulation for Binary Neural Networks](https://mlsanity.com/paper/2107.02751/) (2021)
- [Learning to Hash with Binary Deep Neural Network](https://mlsanity.com/paper/1607.05140/) (2016)
- [Facial Feature Tracking under Varying Facial Expressions and Face Poses based on Restricted Boltzmann Machines](https://mlsanity.com/paper/1709.05731/) (2017)
- [A Generative Restricted Boltzmann Machine Based Method for High-Dimensional Motion Data Modeling](https://mlsanity.com/paper/1710.07831/) (2017)

## Built on by (most cited first, 1 of 1)

- [Quantum-enhanced Computer Vision: Going Beyond Classical Algorithms](https://mlsanity.com/paper/2510.07317/) (2025)

## Abstract (arXiv)

A successful application of quantum annealing to machine learning is training restricted Boltzmann machines (RBM). However, many neural networks for vision applications are feedforward structures, such as multilayer perceptrons (MLP). Backpropagation is currently the most effective technique to train MLPs for supervised learning. This paper aims to be forward-looking by exploring the training of MLPs using quantum annealers. We exploit an equivalence between MLPs and energy-based models (EBM), which are a variation of RBMs with a maximum conditional likelihood objective. This leads to a strategy to train MLPs with quantum annealers as a sampling engine. We prove our setup for MLPs with sigmoid activation functions and one hidden layer, and demonstrated training of binary image classifiers on small subsets of the MNIST and Fashion-MNIST datasets using the D-Wave quantum annealer. Although problem sizes that are feasible on current annealers are limited, we obtained comprehensive results on feasible instances that validate our ideas. Our work establishes the potential of quantum computing for training MLPs.